If the cuts are at or near the soil, your plants are probably being attacked by cutworms. Sometimes in early spring, rabbits and even birds will snip plants off, but generally rabbits eat everything to the ground and birds tend to carry off the snipped pieces. When the sheared-off plant clippings are left laying there, it's likely cutworm damage. The best and safest treatment for cutworms is Bt, Bacillus thuringiensis. It's a natural bacteria that is toxic to cutworms and all caterpillars. Bt is available at garden centers.